How much faster does volume increase compared to surface area?

Answer 1

Hi,

In general when something becomes larger, the surface area to volume ratio decreases. The analogy of a cube is indeed a useful way to think about it. I'll try to put it in more general terms.

Cubes are a great example to talk about because their surface area and volume are really easy to calculate. The surface area of a cube is the length x the width x the number of sides (six sides, in the case of a cube). The volume of a cube is the length x width x volume.

So, say we have a cube with a side length of three. The surface area is going to be 3x3x6 = 54. The volume is going to be 3x3x3 = 27, for a ratio of 54:27, or 2:1

//Another contributor does not think you should make a ratio of different dimensions (area and volume)//

Surface area increases as the square of a dimension, volume increases as the cube of a dimension.

Example:

A sphere (ball)

Diameter = 1 unit

Increase diameter to twice the size: New diameter = 2

Area of new sphere = 4 times the area of the initial sphere

Volume of the new sphere = 8 times the volume of the initial sphere